The idea that big small states are necessarily made worse off by the Electoral College is not correct. See the
Banzhaf power index. When states are larger, they have disproportionately more power to swing an election. Consider if a single state had over 50% of the electoral votes. It would have 100% of the voting power, with the other states entirely irrelevant. Smaller amounts give less extreme examples.
However, I don't believe in the Electoral College. The arguments that cities will simply outvote rural areas usually depend on unrealistic assumptions of people voting in blocs solely as a result of their place of residence. Even if this were the case, you could just end up with the inverse of the malapportioned minority outvoting the majority. Finally, if this is such a good idea, why not apply it to all statewide elections, or even all elections? Why not even have mini-Electoral Colleges inside the Electoral College? If it's so terrible that New York City would be influential in a popular vote election, why is it not also terrible that New York City can outvote Upstate New York in the race for its Electoral Votes?